Answer:
[tex]\Large\boxed{\sf x = 19.2}[/tex]
Step-by-step explanation:
Here a right angled triangle is given to us and we need to find out the value of x . The measure of one of the sides is 24 and one of the acute angle is 53° .
- Here 24 is hypotenuse of the triangle and x is the perpendicular .
So here we may use the ratio of sine as ,
[tex]\sf\qquad\longrightarrow sin\theta =\dfrac{p}{h} \\\\[/tex]
• On substituting the respective values ,
[tex]\sf\qquad\longrightarrow sin53^\circ =\dfrac{x}{24}\\\\[/tex]
Substitute the value of sin 53° = 4/5 ,
[tex]\sf\qquad\longrightarrow \dfrac{4}{5}=\dfrac{x}{24} \\\\[/tex]
Cross multiply ,
[tex]\sf\qquad\longrightarrow x =\dfrac{24*4}{5} \\\\[/tex]
Simplify,
[tex]\sf\qquad\longrightarrow \frak{\pink{x =19.2}} \\\\[/tex]
[tex]\rule{200}4[/tex]
